Mass-Independent Scheme to Test the Quantumness of a Massive Object.

The search for empirical schemes to evidence the nonclassicality of large masses is a central quest of current research. However, practical schemes to witness the irreducible quantumness of an arbitrarily large mass are still lacking. To this end, we incorporate crucial modifications to the standard tools for probing the quantum violation of the pivotal classical notion of macrorealism (MR): while usual tests use the same measurement arrangement at successive times, here we use two different measurement arrangements. This yields a striking result: a mass-independent violation of MR is possible for harmonic oscillator systems. In fact, our adaptation enables probing quantum violations for literally any mass, momentum, and frequency. Moreover, coarse-grained position measurements at an accuracy much worse than the standard quantum limit, as well as knowing the relevant parameters only to this precision, without requiring them to be tuned, suffice for our proposal. These should drastically simplify the experimental effort in testing the nonclassicality of massive objects ranging from atomic ions to macroscopic mirrors in LIGO.

Measuring gravity with milligram levitated masses.

Gravity differs from all other known fundamental forces because it is best described as a curvature of space-time. For that reason, it remains resistant to unifications with quantum theory. Gravitational interaction is fundamentally weak and becomes prominent only at macroscopic scales. This means, we do not know what happens to gravity in the microscopic regime where quantum effects dominate and whether quantum coherent effects of gravity become apparent. Levitated mechanical systems of mesoscopic size offer a probe of gravity, while still allowing quantum control over their motional state. This regime opens the possibility of table-top testing of quantum superposition and entanglement in gravitating systems. Here, we show gravitational coupling between a levitated submillimeter-scale magnetic particle inside a type I superconducting trap and kilogram source masses, placed approximately half a meter away. Our results extend gravity measurements to low gravitational forces of attonewton and underline the importance of levitated mechanical sensors.

Collapse Models: A Theoretical, Experimental and Philosophical Review.

In this paper, we review and connect the three essential conditions needed by the collapse model to achieve a complete and exact formulation, namely the theoretical, the experimental, and the ontological ones. These features correspond to the three parts of the paper. In any empirical science, the first two features are obviously connected but, as is well known, among the different formulations and interpretations of non-relativistic quantum mechanics, only collapse models, as the paper well illustrates with a richness of details, have experimental consequences. Finally, we show that a clarification of the ontological intimations of collapse models is needed for at least three reasons: (1) to respond to the indispensable task of answering the question 'what are collapse models (and in general any physical theory) about?'; (2) to achieve a deeper understanding of their different formulations; (3) to enlarge the panorama of possible readings of a theory, which historically has often played a fundamental heuristic role.

Levitated Micromagnets in Superconducting Traps: A New Platform for Tabletop Fundamental Physics Experiments.

Magnetically levitated microparticles have been proposed as mechanical sensors with extreme sensitivity. In particular, micromagnets levitated above a superconductor can achieve very low levels of dissipation and thermal noise. In this paper, we review recent initial experiments and discuss the potential for using these systems as sensors of magnetic fields and rotational motion, as well as possible applications to fundamental physics.

Quantum technologies in space.

Recently, the European Commission supported by many European countries has announced large investments towards the commercialization of quantum technology (QT) to address and mitigate some of the biggest challenges facing today's digital era - e.g. secure communication and computing power. For more than two decades the QT community has been working on the development of QTs, which promise landmark breakthroughs leading to commercialization in various areas. The ambitious goals of the QT community and expectations of EU authorities cannot be met solely by individual initiatives of single countries, and therefore, require a combined European effort of large and unprecedented dimensions comparable only to the Galileo or Copernicus programs. Strong international competition calls for a coordinated European effort towards the development of QT in and for space, including research and development of technology in the areas of communication and sensing. Here, we aim at summarizing the state of the art in the development of quantum technologies which have an impact in the field of space applications. Our goal is to outline a complete framework for the design, development, implementation, and exploitation of quantum technology in space.

Surpassing the Energy Resolution Limit with Ferromagnetic Torque Sensors.

We discuss the fundamental noise limitations of a ferromagnetic torque sensor based on a levitated magnet in the tipping regime. We evaluate the optimal magnetic field resolution taking into account the thermomechanical noise and the mechanical detection noise at the standard quantum limit. We find that the energy resolution limit, pointed out in recent literature as a relevant benchmark for most classes of magnetometers, can be surpassed by many orders of magnitude. Moreover, similarly to the case of a ferromagnetic gyroscope, it is also possible to surpass the standard quantum limit for magnetometry with independent spins, arising from spin-projection noise. Our finding indicates that magnetomechanical systems optimized for magnetometry can achieve a magnetic field resolution per unit volume several orders of magnitude better than any conventional magnetometer. We discuss possible implications, focusing on fundamental physics problems such as the search for exotic interactions beyond the standard model.

Zel'dovich Amplification in a Superconducting Circuit.

Zel'dovich proposed that electromagnetic (EM) waves with angular momentum reflected from a rotating metallic, lossy cylinder will be amplified. However, we are still lacking a direct experimental EM-wave verification of this fifty-year-old prediction due to the challenging conditions in which the phenomenon manifests itself: the mechanical rotation frequency of the cylinder must be comparable with the EM oscillation frequency. Here, we propose an experimental approach that solves this issue and is predicted to lead to a measurable Zel'dovich amplification with existing superconducting circuit technology. We design a superconducting circuit with low frequency EM modes that couple through free space to a magnetically levitated and spinning microsphere placed at the center of the circuit. We theoretically estimate the circuit EM mode gain and show that rotation of the microsphere can lead to experimentally observable amplification, thus paving the way for the first EM-field experimental demonstration of Zel'dovich amplification.

Detecting Acceleration-Enhanced Vacuum Fluctuations with Atoms Inside a Cavity.

Some of the most prominent theoretical predictions of modern times, e.g., the Unruh effect, Hawking radiation, and gravity-assisted particle creation, are supported by from the fact that various quantum constructs like particle content and vacuum fluctuations of a quantum field are observer-dependent. Despite being fundamental in nature, these predictions have not yet been experimentally verified because one needs extremely strong gravity (or acceleration) to bring them within the existing experimental resolution. In this Letter, we demonstrate that a post-Newtonian rotating atom inside a far-detuned cavity experiences strongly modified quantum fluctuations in the inertial vacuum. As a result, the emission rate of an excited atom gets enhanced significantly along with a shift in the emission spectrum due to the change in the quantum correlation under rotation. We propose an optomechanical setup that is capable of realizing such acceleration-induced particle creation with current technology. This provides a novel and potentially feasible experimental proposal for the direct detection of noninertial quantum field theoretic effects.

Photon Bunching in a Rotating Reference Frame.

Although quantum physics is well understood in inertial reference frames (flat spacetime), a current challenge is the search for experimental evidence of nontrivial or unexpected behavior of quantum systems in noninertial frames. Here, we present a novel test of quantum mechanics in a noninertial reference frame: we consider Hong-Ou-Mandel (HOM) interference on a rotating platform and study the effect of uniform rotation on the distinguishability of the photons. Both theory and experiments show that the rotational motion induces a relative delay in the photon arrival times at the exit beam splitter and that this delay is observed as a shift in the position of the HOM dip. This experiment can be extended to a full general relativistic test of quantum physics using satellites in Earth's orbit and indicates a new route toward the use of photonic technologies for investigating quantum mechanics at the interface with relativity.

Precession Motion in Levitated Optomechanics.

We investigate experimentally the dynamics of a nonspherical levitated nanoparticle in a vacuum. In addition to translation and rotation motion, we observe the light torque-induced precession and nutation of the trapped particle. We provide a theoretical model, which we numerically simulate and from which we derive approximate expressions for the motional frequencies. Both the simulation and approximate expressions we find in good agreement with experiments. We measure a torque of 1.9±0.5×10^{-23} N m at 1×10^{-1} mbar, with an estimated torque sensitivity of 3.6±1.1×10^{-31} N m/sqrt[Hz] at 1×10^{-7} mbar.

Spin Entanglement Witness for Quantum Gravity.

Understanding gravity in the framework of quantum mechanics is one of the great challenges in modern physics. However, the lack of empirical evidence has lead to a debate on whether gravity is a quantum entity. Despite varied proposed probes for quantum gravity, it is fair to say that there are no feasible ideas yet to test its quantum coherent behavior directly in a laboratory experiment. Here, we introduce an idea for such a test based on the principle that two objects cannot be entangled without a quantum mediator. We show that despite the weakness of gravity, the phase evolution induced by the gravitational interaction of two micron size test masses in adjacent matter-wave interferometers can detectably entangle them even when they are placed far apart enough to keep Casimir-Polder forces at bay. We provide a prescription for witnessing this entanglement, which certifies gravity as a quantum coherent mediator, through simple spin correlation measurements.

Effects of Newtonian gravitational self-interaction in harmonically trapped quantum systems.

The Schrödinger-Newton equation has gained attention in the recent past as a nonlinear modification of the Schrödinger equation due to a gravitational self-interaction. Such a modification is expected from a fundamentally semi-classical theory of gravity and can, therefore, be considered a test case for the necessity of the quantisation of the gravitational field. Here we provide a thorough study of the effects of the Schrödinger-Newton equation for a micron-sized sphere trapped in a harmonic oscillator potential. We discuss both the effect on the energy eigenstates and the dynamical behaviour of squeezed states, covering the experimentally relevant parameter regimes.

Experimental Realization of a Thermal Squeezed State of Levitated Optomechanics.

We experimentally squeeze the thermal motional state of an optically levitated nanosphere by fast switching between two trapping frequencies. The measured phase-space distribution of the center of mass of our particle shows the typical shape of a squeezed thermal state, from which we infer up to 2.7 dB of squeezing along one motional direction. In these experiments the average thermal occupancy is high and, even after squeezing, the motional state remains in the remit of classical statistical mechanics. Nevertheless, we argue that the manipulation scheme described here could be used to achieve squeezing in the quantum regime if preceded by cooling of the levitated mechanical oscillator. Additionally, a higher degree of squeezing could, in principle, be achieved by repeating the frequency-switching protocol multiple times.

Visualisation of quantum evolution in the Stern-Gerlach and Rabi experiments.

The Stern-Gerlach experiment is a seminal experiment in quantum physics, involving the interaction between a particle with spin and an applied magnetic field gradient. A recent article [Wennerström et al., Phys. Chem. Chem. Phys., 2012, 14, 1677-1684] claimed that a full understanding of the Stern-Gerlach experiment can only be attained if transverse spin relaxation is taken into account, generated by fluctuating magnetic fields originating in the magnetic materials which generate the field gradient. This interpretation is contrary to the standard quantum description of the Stern-Gerlach experiment, which requires no dissipative effects. We present simulations of conventional quantum dynamics in the Stern-Gerlach experiment, using extended Wigner functions to describe the propagation of the quantum state in space and time. No relaxation effects are required to reproduce the qualitative experimental behaviour. We also present simulations of quantum dynamics in the Rabi experiment, in which an applied radiofrequency field induces spin transitions in the particle wave.

A proposal for the experimental detection of CSL induced random walk.

Continuous Spontaneous Localization (CSL) is one possible explanation for dynamically induced collapse of the wave-function during a quantum measurement. The collapse is mediated by a stochastic non-linear modification of the Schrödinger equation. A consequence of the CSL mechanism is an extremely tiny violation of energy-momentum conservation, which can, in principle, be detected in the laboratory via the random diffusion of a particle induced by the stochastic collapse mechanism. In a paper in 2003, Collett and Pearle investigated the translational CSL diffusion of a sphere, and the rotational CSL diffusion of a disc, and showed that this effect dominates over the ambient environmental noise at low temperatures and extremely low pressures (about ten-thousandth of a pico-Torr). In the present paper, we revisit their analysis and argue that this stringent condition on pressure can be relaxed, and that the CSL effect can be seen at the pressure of about a pico-Torr. A similar analysis is provided for diffusion produced by gravity-induced decoherence, where the effect is typically much weaker than CSL. We also discuss the CSL induced random displacement of a quantum oscillator. Lastly, we propose possible experimental set-ups justifying that CSL diffusion is indeed measurable with the current technology.

On the existence of low-mass dark matter and its direct detection.

Dark Matter (DM) is an elusive form of matter which has been postulated to explain astronomical observations through its gravitational effects on stars and galaxies, gravitational lensing of light around these, and through its imprint on the Cosmic Microwave Background (CMB). This indirect evidence implies that DM accounts for as much as 84.5% of all matter in our Universe, yet it has so far evaded all attempts at direct detection, leaving such confirmation and the consequent discovery of its nature as one of the biggest challenges in modern physics. Here we present a novel form of low-mass DM χ that would have been missed by all experiments so far. While its large interaction strength might at first seem unlikely, neither constraints from particle physics nor cosmological/astronomical observations are sufficient to rule out this type of DM, and it motivates our proposal for direct detection by optomechanics technology which should soon be within reach, namely, through the precise position measurement of a levitated mesoscopic particle which will be perturbed by elastic collisions with χ particles. We show that a recently proposed nanoparticle matter-wave interferometer, originally conceived for tests of the quantum superposition principle, is sensitive to these collisions, too.

Near-field interferometry of a free-falling nanoparticle from a point-like source.

Matter-wave interferometry performed with massive objects elucidates their wave nature and thus tests the quantum superposition principle at large scales. Whereas standard quantum theory places no limit on particle size, alternative, yet untested theories--conceived to explain the apparent quantum to classical transition--forbid macroscopic superpositions. Here we propose an interferometer with a levitated, optically cooled and then free-falling silicon nanoparticle in the mass range of one million atomic mass units, delocalized over >150 nm. The scheme employs the near-field Talbot effect with a single standing-wave laser pulse as a phase grating. Our analysis, which accounts for all relevant sources of decoherence, indicates that this is a viable route towards macroscopic high-mass superpositions using available technology.

Optomechanical interface for probing matter-wave coherence.

We combine matter-wave interferometry and cavity optomechanics to propose a coherent matter-light interface based on mechanical motion at the quantum level. We demonstrate a mechanism that is able to transfer non-classical features imprinted on the state of a matter-wave system to an optomechanical device, transducing them into distinctive interference fringes. This provides a reliable tool for the inference of quantum coherence in the particle beam. Moreover, we discuss how our system allows for intriguing perspectives, paving the way to the construction of a device for the encoding of quantum information in matter-wave systems. Our proposal, which highlights previously unforeseen possibilities for the synergistic exploitation of these two experimental platforms, is explicitly based on existing technology, available and widely used in current cutting-edge experiments.

Experimental methods of molecular matter-wave optics.

We describe the state of the art in preparing, manipulating and detecting coherent molecular matter. We focus on experimental methods for handling the quantum motion of compound systems from diatomic molecules to clusters or biomolecules.Molecular quantum optics offers many challenges and innovative prospects: already the combination of two atoms into one molecule takes several well-established methods from atomic physics, such as for instance laser cooling, to their limits. The enormous internal complexity that arises when hundreds or thousands of atoms are bound in a single organic molecule, cluster or nanocrystal provides a richness that can only be tackled by combining methods from atomic physics, chemistry, cluster physics, nanotechnology and the life sciences.We review various molecular beam sources and their suitability for matter-wave experiments. We discuss numerous molecular detection schemes and give an overview over diffraction and interference experiments that have already been performed with molecules or clusters.Applications of de Broglie studies with composite systems range from fundamental tests of physics up to quantum-enhanced metrology in physical chemistry, biophysics and the surface sciences.Nanoparticle quantum optics is a growing field, which will intrigue researchers still for many years to come. This review can, therefore, only be a snapshot of a very dynamical process.